Multi-Modal Type-Logical Grammar∗

Our focus in this chapter is on grammatical composition, the relation that holds (relative to a formal or cognitive system of grammatical analysis G) between the global properties associated with a linguistic entity and the correlative properties associated with its component parts. We first discuss why grammatical composition in this sense raises questions that deserve particular attention. We then show that the problem of grammatical composition has the form of an inference problem, with the components of an expression playing the role of premisses and the global analysis of the expression as a whole playing the role of a conclusion licensed by those premisses in some system of grammatical deduction. But an appropriate system of inference, while similar in some ways to such (possibly) familiar systems as classical and intuition-istic propositional logic, differs from these reasoning systems in fundamental ways. First, it is resource-sensitive, meaning that it depends not only what premisses are present, but on their multi-plicity and structural arrangement. Second, it manifests a form of 4 self-contained inferential control, meaning that parametric options concerning structural communication among resource-premisses can be accessed selectively by appropriate type declarations, rather than serving as absolute, global, all-or-nothing choices. The logical perspective informing this point of view is not generally familiar to working grammarians. But since logical proof-theory is essentially syntactic in nature, the syntax of proofs on which our presentation is based will be quite accessible to readers with a background in theoretical syntax. Moreover, the issues of resource-structure and resource-management that we shall discuss arise across the spectrum of currently available grammatical frameworks, in ways that we hope will be recognizable. Accordingly, we shall endeavor in what follows to display the conceptual choices that present themselves to anyone who wishes to pursue this line of linguistic enquiry , and to examine in some depth how particular choices yield insightful models of a modest range of linguistic phenomena. The claim of grammatical composition on our attention can be justified by considering the following claims: 1. Linguistic entities are associated with physical correlates: physical objects such as written marks, physical events such as speech or signing. 2. The physical correlates of linguistic entities have the remarkable quality that they systematically support an extraordinary range of symbolic interpretations. 3. The symbolic properties of linguistic (2) entities cannot be identified with their physical correlates (1). To see this, simply note that a single physical correlate …